Overview of Cryptography

Contents in Brief

  • 1.1 Introduction............................. 1
  • 1.2 Information security and cryptography .............. 2
  • 1.3 Background on functions...................... 6
  • 1.4 Basic terminology and concepts................... 11
  • 1.5 Symmetric-key encryption..................... 15
  • 1.6 Digital signatures.......................... 22
  • 1.7 Authentication and identification.................. 24
  • 1.8 Public-key cryptography...................... 25
  • 1.9 Hash functions........................... 33
  • 1.10 Protocols and mechanisms..................... 33
  • 1.11 Key establishment, management, and certification......... 35
  • 1.12 Pseudorandom numbers and sequences.............. 39
  • 1.13 Classes of attacks and security models............... 41
  • 1.14 Notes and further references.................... 45

Introduction

Cryptography has a long and fascinating history. The most complete non-technical account of the subject is Kahn’s The Codebreakers. This book traces cryptography from its initial and limited use by the Egyptians some 4000 years ago, to the twentieth century where it played a crucial role in the outcome of both world wars. Completed in 1963, Kahn’s book covers those aspects of the history' which were most significant (up to that time) to the development of the subject. The predominant practitioners of the art were those associated with the military', the diplomatic service and government in general. Cryptography was used as a tool to protect national secrets and strategies.

The proliferation of computers and communications systems in the 1960s brought with it a demand from the private sector for means to protect information in digital form and to provide security services. Beginning with the work of Feistel at IBM in the early 1970s and culminating in 1977 with the adoption as a U.S. Federal Information Processing Standard for encrypting unclassified information, DES, the Data Encryption Standard, is the most well-known cryptographic mechanism in history. It remains the standard means for securing electronic commerce for many financial institutions around the world.

The most striking development in the history' of cryptography came in 1976 when Diffie and Heilman published New Directions in Cryptography. This paper introduced the revolutionary concept of public-key cryptography and also provided a new and ingenious method for key exchange, the security of which is based on the intractability of the discrete logarithm problem. Although the authors had no practical realization of a public-key encryption scheme at the time, the idea was clear and it generated extensive interest and activity in the cryptographic community. In 1978 Rivest, Shamir, and Adleman discovered the first practical public-key encryption and signature scheme, now referred to as RSA. The RSA scheme is based on another hard mathematical problem, the intractability of factoring large integers. This application of a hard mathematical problem to cryptography revitalized efforts to find more efficient methods to factor. The 1980s saw major advances in this area but none which rendered the RSA system insecure. Another class of powerful and practical public-key schemes was found by ElGamal in 1985. These are also based on the discrete logarithm problem.

One of the most significant contributions provided by public-key cryptography is the digital signature. In 1991 the first international standard for digital signatures (ISO/IEC 9796) was adopted. It is based on the RSA public-key scheme. In 1994 the U.S. Government adopted the Digital Signature Standard, a mechanism based on the ElGamal public- key scheme.

The search for new public-key schemes, improvements to existing cryptographic mechanisms, and proofs of security continues at a rapid pace. Various standards and infrastructures involving cryptography are being put in place. Security products are being developed to address the security needs of an information intensive society.

The purpose of this book is to give an up-to-date treatise of the principles, techniques, and algorithms of interest in cryptographic practice. Emphasis has been placed on those aspects which are most practical and applied. The reader will be made aware of the basic issues and pointed to specific related research in the literature where more indepth discussions can be found. Due to the volume of material which is covered, most results will be stated without proofs. This also serves the purpose of not obscuring the very applied nature of the subject. This book is intended for both implementers and researchers. It describes algorithms, systems, and their interactions.

Chapter 1 is a tutorial on the many and various aspects of cryptography. It does not attempt to convey all of the details and subtleties inherent to the subject. Its purpose is to introduce the basic issues and principles and to point the reader to appropriate chapters in the book for more comprehensive treatments. Specific techniques are avoided in this chapter.

 
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